GATE EE 2015 Question Paper (07-Feb-2015) (Shift 2)

Two identical coils each having inductance $L$ are placed together on the same core. If an overall inductance of $\alpha L$ is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: $N_1=100,N_2=50,N_3=50$. If the magnetizing current is neglected, and the currents in two windings are ${\bar{I}}_2=2\angle 30^{\circ }Aand{\bar{I}}_3=2\angle 150^{\circ }A$, then what is the value of the current ${\bar{I}}_1$ in Ampere?

With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is 1000 rpm, and its armature current is 10 A. The armature resistance is 1 Ω. The load torque of the fan load is proportional to the square of the rotor. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to 500 rpm is

A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is connected to an 11 kV, 50 Hz source. Its synchronous reactance is 50 Ω per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is 100 A at the unity power factor. If the load torque is increased so that the stator current is 120 A, then the load angle (in degrees) at this load is ________.

A 220 V, 3 – phase, 4 – pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225% of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 Ω/phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is__________